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In a previous MITACS project in collaboration with Addenda Capital, two basic liability matching strategies have been investigated: cash flow matching and moment matching. These strategies performed well under a wide variety of tests including historical backtesting. A potential shortcoming for both of these methods is that the optimization process is done only once at the beginning of the investment horizon and uses deterministic moment matching constraints to immunize the portfolio against interest rate movements. Though the portfolio subsequently need to be frquently rebalanced, this static optimization does not take into account the relatively high rebalancing costs it involves. The main objective of this present project is to further enhance the moment matching method by implementing and testing a stochastic dynamic optimization and by comparing its efficiency with the static one. Our dynamic optimization problem is to minimize the portfolio cost and its expected rebalancing costs one month ahead over a set of interest rate scenarios by the use of stochastic moment matching constraints. Our backtesting results show some improvements with the 6 moments matching strategy as the dynamic optimization slightly shrinks the difference in asset-liability gap between scenarios compared with the static optimization. However, after analyzing the realized periodic rebalancing costs each month (a constant bid-ask spread has been assigned to each asset's position change in the optimal portfolio), the immunization improvements are mitigated by substantialy higher costs. We also noticed, in the case of the duration/convexity matching strategy, that the dynamic optimization is not that much more efficient than the static method. Thus, these results confirm that the 6 moments matching technique is still more efficient with both the static and stochastic dynamic optimization. Our extensive dynamic analysis of transaction costs through backtesting showed that from an efficiency to cost ratio and an efficiency to simplicity ratio, the static 6 moments matching method seems so far to be a more practical solution for liability matching.